The determinant of a 2x2 matrix

Cramer’s method provides a direct formula for the solutions, using determinants. It is especially convenient for $2\times 2$ systems.

Definition — Determinant of a $2\times 2$ matrix

Given the $2\times 2$ system $\begin{cases} a_1 x + b_1 y = c_1 \\ a_2 x + b_2 y = c_2 \end{cases}$ the determinant of the coefficient matrix is: $\Delta = \begin{vmatrix} a_1 & b_1 \\ a_2 & b_2 \end{vmatrix} = a_1 b_2 - b_1 a_2.$

The determinant is therefore a number: it is obtained from the product of the elements on the main diagonal minus the product of those on the other diagonal.

Connections

Topics: Linear systems
Concepts: Determinant · 2x2 linear system
Skills: Using formulae